Interference measuring device

ABSTRACT

In an interference measuring device, which includes: a coherent beam generating source; a sample to be measured; a lens system for forming an image of the sample to be measured on an observing plane; an interference element for splitting a coherent beam into two systems, and forming an interference image on the observing plane or a plane equivalent thereto; an image pickup element for picking up the interference image on the observing plane; and a calculating device having functions of capturing and storing the interference image converted to electric signals by the image pickup element, and determining the phase distribution changed by the sample to be measured from the interference image by calculation, wherein a means for removing the phase change distribution due to the interference element is provided.

BACKGROUND OF THE INVENTION

[0001] The present invention particularly relates to an interferencemeasuring device belonging to a wavefront splitting type amonginterference measuring devices.

[0002] The interferometers often used for interference measurement usinga laser include: Twyman-Green interferometer (ex., reference literature1: Subfringe Interference Measurement Basic Theory, Optics 13 (1984)p.p. 55-65, or reference literature 2: Quantitative Phase Analysis inElectron Holographic Interferometry, Appl. Opt. 26 (1987) 377-382),Mach-Zehnder interferometer (reference literature 3: InterferenceElectron Microscopy by Means of Holography, Japan, J. Appl. Phys. 18(1979) 2291-2294), further, Fizeau interferometer (reference literature4: High Resolution Phase Measuring Laser Interferometric Microscope forEngineering Surface Metrology, SPIE 1009 (1988) 35-44), and the like.Any of the interferometers is of an amplitude splitting type whichsplits one beam into two beams, a beam transmitted through asemitransparent mirror and a beam reflected thereby.

[0003] On the other hand, also in the field of an electron beam, a studyhas been made on the measurement of not only the shape of an object butalso the distribution of the electromagnetic field in the vicinity of asample utilizing the phase information of an electron wave. The electronbeam interferometer practically includes only an electron beam biprism(ex., reference literature 5: New Development in Electron InterferenceMeasurement, Electron Microscopy 30 (1995) 113-120), referenceliterature 6: Japanese Laid-Open Patent Publication No. Hei 10-199464,and reference literature 7: Japanese Laid-Open Patent Publication No.Hei 11-40097). It is of a wavefront splitting type which spatiallysplits a beam into two beams, for example, a right-half beam and aleft-half beam. There are not many cases where the wavefront splittingtype is used for optical interference measurement.

[0004] In interference measurement, a beam changed in phase by a sampleto be measured and a reference beam are allowed to interfere with eachother to form an interference image. The distribution of phase changesdue to the sample to be measured is examined from the resultinginterference image. The information obtained from the distribution ofphase changes varies according to the construction of the interferencesystem. In the field of laser optics, the most common case is where theinformation is applied to the measurements of the surface precision andshape of the surface, unevenness of the thickness, and the like, of thesample to be measured. In the field of electron interference, themeasurement of the distribution of electromagnetic field is also animportant application other than the measurement of the shape of thesample to be measured.

[0005] As a method for calculating the distribution of phase changesfrom the interference image, for example, mention may be made of thefollowing method. One interference image is inputted and stored into acalculating device via an image pickup element and an image captureboard. This is mathematically Fourier transformed, so that there occur±primary spectra corresponding to the basic interference fringesdetermined by the angle formed between two interfering luminous fluxesand the directions thereof with the center of the Fourier spectrumdiagram as a center of point symmetry. The phase-changed components dueto the sample are distributed around the +primary and −primary spectra,which are equivalent to each other. Therefore, one spectrum is selectedwith a window having a proper size to be Fourier inverse transformed. Asa result, the distribution of phase is reproduced.

[0006] The phase distribution includes the tilt components due to theangle formed between the two luminous fluxes which have been allowed tointerfere with each other. Therefore, the selected spectrum is shiftedto the origin point, and then Fourier inverse transformed, or it isFourier inverse transformed, and then the tilt component is corrected.As a result, it is possible to determine the distribution of phaseschanged by the sample.

[0007] The method most commonly used for a high-precision interferencemeasurement is the fringe scanning method (also referred to as a phaseshift method, in section 3.2 on page 58 of the reference literature 1).The detail of the measurement principle of this method is described onpages 58 to 59 of the reference literature 1, and hence a detaileddescription thereon is omitted. To be brief, the measurement principleis as follows.

[0008] With this method, in general, only the conditions for forminginterference fringes are changed, so that the resulting interferenceimage is recorded while successively shifting the relative phasedifference between an object wave and a reference wave at an observingplane by a 1/M the wavelength (M is a positive integer of 3 or more).From the recorded M-interference-image group data, the distributionφ(x,y) of the phases changed by the sample is expressed as the followingequation (1): $\begin{matrix}{{\varphi \left( {x,y} \right)} = {\tan^{- 1}\left\lbrack \frac{\sum\limits_{m = 1}^{M}{{I\left( {x,{y;m}} \right)}{\sin \left( \frac{2\pi \quad n}{M} \right)}}}{\sum\limits_{m = 1}^{M}{{I\left( {x,{y;m}} \right)}{\cos \left( \frac{2\pi \quad m}{M} \right)}}} \right\rbrack}} & (1)\end{matrix}$

[0009] where I(x,y;m) denotes the intensity distribution of theinterference image captured for the m-th time. The relative phasedifference between the object wave and the reference wave is generallychanged in the following manner. A reflecting mirror or asemitransparent mirror is micro-moved by a piezoelectrically drivenstage, or the like, thereby to change the optical path length of thereference beam. This method is also used for electron interference. Inthis case, the relative phase difference between the object wave and thereference wave is changed in the following manner. Namely, an electronbeam biprism is moved, or the tilt of the beam to be irradiated onto asample to be measured is changed.

[0010] In the field of laser optics, high-precision interferencemeasuring devices are mostly of a reflection type on the order of equalmagnification, and there are less examples of microscopes of areflection type (the reference literature 4). There are further lessexamples of transmission type microscopes, although there is the exampleof Mach-Zehnder interferometer using a Koster prism (referenceliterature 8: Quantitative measurement of a phase object by fringescanning interference microscopy, Appl. Opt. 28 (1989) 1615-1617). Inany of these examples, splitting of beams is accomplished based on theamplitude splitting type. In the field of electron beam, in most cases,the wavefront splitting type and transmission type microscopes areemployed from the restriction of the interferometer.

[0011] Also in the field of laser optics, the configuration of atransmission type microinterferometer system based on the wavefrontsplitting mode has a large merit. With the transmission typemicrointerferometer system, although the beam transmitted through thesample is enlarged by the use of a lens system, the reference beam isalso required to be enlarged simultaneously. With the transmission typemicrointerferometer system of the amplitude splitting mode, the twosplit luminous fluxes pass through largely different paths, and hencetend to be affected by vibration. Thus, a very large magnifying lens isrequired to be inserted, alternatively, the same magnifying systems arerequired to be inserted to their respective optical paths as in thereference literature 8. In contrast, with the wavefront splitting mode,the two luminous fluxes pass through almost the same paths, and hencethey are less susceptible to vibration. Accordingly, only one system isrequired as the magnifying lens system.

[0012] In order to carry out the fringe scanning method with theinterference system of the wavefront splitting type, the relativepositional relationship between a sample image and interference fringesis required to be shifted on the observing plane. To do this, forexample, the following methods are conceivable.

[0013] 1. The wavefront splitting element is moved in the directionorthogonal to the wavefront splitting boundary;

[0014] 2. The tilt of the exposure beam is changed in the directionorthogonal to the wavefront splitting boundary;

[0015] 3. The refractive index of the wavefront splitting element ischanged;

[0016] 4. A phase modulation element (ex., liquid crystal plate) isinserted in at least one of the object wave or the reference wave tochange the phase; and

[0017] 5. When alignment is performed in the calculating device, thesample is moved with the interference conditions left unchanged. Thefirst, second, and fifth methods can be readily applied to any of thelaser interference system and the electron beam interference system.However, the third method and the fourth method are practicallydifficult to be applied to the laser interference system and theelectron beam interference system, respectively.

[0018]FIG. 1 shows an example of a configuration of a wavefrontsplitting type fringe scanning laser interference measuring device. Inthis example, there is shown a method in which a biprism 5 which is awavefront splitting element is moved, thereby to change the relativepositional relationship between a sample image and interference fringes.A beam emitted from a coherent beam source (a laser in this case) 1 isconverted to a parallel light by collimator lenses 2 and 3, andirradiated to a sample 10. When the sample 10 is small, the collimatorlenses are not necessarily required. The transmission image of thesample 10 is formed on an observing plane 21 by using an objective lens4. In this example, the image is formed directly on the image pickupsurface of an image pickup element 20. The beam transmitted through thesample 10 (the portion of the dotted area in the figure) 11 has beenchanged in phase according to the distribution of the refractive indexfor the exposure beam in the sample. A wavefront splitting element intriangle pole (herein, also referred to as a biprism) 5 is placed at anappropriate position between the objective lens 4 and the observingplane 21. Thus, the beam transmitted through the sample 10 (hatchingslanting downwardly to the right: generally referred to as an objectwave) 12 passes through the focal point of the objective lens 4, andthen, passes through the upper part of the biprism 5 to be deflectedcloser to an optical axis 13. Whereas, the beam passed through the partwhere there is no sample (hatching portion slanting upwardly to theright: generally referred to as a reference wave) 14 is deflected in theopposite direction. As a result, interference fringes are formed at theoverlapping portion of both (crosshatching portion) 15. On the observingplane 21, there occur linear interference fringes in the sample-lessportion. Whereas, there are observed interference fringes deviated fromstraight lines in proportional to the phase distribution of thetransmission beam.

[0019] A reference numeral 30 denotes a monitor for image observation.It converts a signal from the image pickup element 20 into an image, anddisplays it. A reference numeral 50 denotes a calculating device, towhich a monitor for a calculating device 60 is connected. Thus, itperforms the operation and management of a laser interference system. Areference numeral 51 denotes an image capture board, which is aninterface for capturing a signal from the monitor 30 for imageobservation into the calculating device 50. Incidentally, the monitor 30for image observation is capable of also serving as the monitor 60 for acalculating device. On the monitor for image observation 30, as with thecase on the observing plane 20, there occur linear interference fringesin the sample-less portion, while there are observed interferencefringes shifted in accordance with the phase distribution of thetransmission beam in the sample-including portion.

[0020] In order to carry out the fringe scanning interferometry, herein,a signal is sent to a micro-movement control device 40 in response to aninstruction via the calculating device 50 from an observer, so that amicro-movement control mechanism 41 by a piezo element is micro-moved.Accordingly, the biprism 5 is moved in the direction orthogonal to boththe optical axis 13 and the wavefront splitting boundary of the biprism5, i.e., in the upward or downward direction in the figure. For example,when the biprism 5 is micro-moved upwardly, the object wave 12 passesthrough the thicker portion of glass of the biprism 5, and hence it isdelayed in phase. Whereas, the reference wave 14 passes through thethinner portion, and hence it is advanced in phase. FIG. 2 shows themanner in which the object wave and the reference wave interfere witheach other in this case.

[0021] The laser light indicated by an arrow A is the object wave 12transmitted through the sample 10. Each of the wavefronts 12 ₁, 12 ₂, .. . has an uneven shape in accordance with the distribution ofrefractive index in the sample 10. On the other hand, the laser lightindicated by an arrow B is a reference plane wave, and the wavefrontsare indicated by a line group 13 ₁, 13 ₂, . . . in the figure. When thelaser light A and the laser light B tilted to the left and right,respectively, each at an angle of θ from the optical axis 13 interferewith each other, they reinforce each other at the region where the leftand right wavefronts cross each other, resulting in a higher intensity.Whereas, they cancel each other at the region where the left and rightwavefronts are superimposed in such a manner as to be shifted from eachother by a half distance, resulting in a lower intensity. As a result,there occur interference fringes with the intensity distribution asindicated by a solid curved line 22.

[0022] At the regions where there is not present the sample 10 as in theopposite left and right edges of FIG. 2, there is the relationshipexpressed by the following equation (2) between the distance d betweeninterference fringes, and the wavelength λ and the tilt θ of the laserlight, and the relationship can be expressed as the equation (3) becausethe θ is generally very small.

2d sin θ=λ  (2)

[0023] $\begin{matrix}{d = \frac{\lambda}{2\theta}} & (3)\end{matrix}$

[0024] Such interference fringes are determined by the interferencesystem, and hence referred to as basic interference fringes or carrierinterference fringes. On the other hand, the interference fringes in theregion where the light rays have transmitted through the sample are notin straight lines, and locally shifted in distance and direction fromthe basic interference fringes in accordance with the phase changes.

[0025] Herein, a consideration will be given to the case where the laserlight B of the reference wave 13 has been slightly advanced in phase.The wavefronts have moved to the positions respectively indicated bybroken lines 13 ₁′, 13 ₂′, and each of the wavefronts crosses thedifferent portion of the object wave 12. Accordingly, the resultinginterference fringes are shifted as indicated by a broken curved line22′. The movement of the interference fringes is determined by therelative positional relationship between the object wave 12 and thereference wave 13, regardless of whether the object wave 12, or both theobject wave 12 and the reference wave 13 are advanced or delayed inphase. Even when the object wave 12 is advanced or delayed in phase, thetilt of the beam due to the biprism 5 is constant, so that the image ofthe sample does not move.

[0026] Thus, every time an interference image wherein the basicinterference fringes have been shifted by 1/M (M: a positive integer of3 or more) of the distance d is formed, the resulting interference imageis captured into the calculating device 50 via the image pickup element20 and the image capture board 51. A group of M interference images thuscaptured are sequentially arranged, indicating that the intensity of thelaser light at a given one point in each of the images changes inaccordance with the sine curve. FIG. 3 schematically shows this statefor M=3, i.e., for three interference images M₁, M₂, and M₃. The amountof phase change is plotted on the abscissa, and the luminance of thelaser light is plotted on the ordinate, thus showing the relationshipwith respective interference images. The reason for limiting the valueof M to 3 or more is that data of 3 points at minimum is required fordetermining the sine curve on one point. The brightness of one point inthe first interference image may start from the peak, or halfway in thevalley according to the position. The phase value measured from theorigin point of the sine curve determined for the point corresponds tothe phase value of the laser light transmitted through the point.Therefore, if this value is determined for each point in theinterference images, it is possible to determine the phase distributiondue to the sample.

[0027] Such a way to determine the phase distribution can bemathematically expressed as the following equation (4), slightlydifferent in description from the foregoing equation (1) due to thepresence of the basic interference fringes: $\begin{matrix}{\left\{ {\frac{2\pi \quad x}{d} + {\varphi \left( {x,y} \right)}} \right\} = {\tan^{- 1}\left\lbrack \frac{\sum\limits_{m = 1}^{M}{{I\left( {x,{y;m}} \right)}{\sin \left( \frac{2\pi \quad m}{M} \right)}}}{\sum\limits_{m = 1}^{M}{{I\left( {x,{y;m}} \right)}{\cos \left( \frac{2\pi \quad m}{M} \right)}}} \right\rbrack}} & (4)\end{matrix}$

[0028] where d denotes the distance between the basic interferencefringes, of which the direction is matched to the direction of y axis.The first term of the left side is the linear tilt resulting from theinterference of two tilted beams. Therefore, it is the already knownamount, and hence it is easy to remove by calculation. Incidentally, themeasurement not using the fringe scanning method is also possible. Insuch a case, one interference image may be captured into the calculatingdevice 50 via the image pickup element 20 and the image capture board51, and calculated by the foregoing Fourier transform method.

[0029] The phase distribution due to the sample determined by thetransmission type microscope is the refractive index distribution forthe laser interference system, and the sample thickness distribution,the internal potential distribution (corresponding to the refractiveindex distribution), and the distribution of electromagnetic fieldinside and outside the sample for the electron beam interference system.

[0030]FIG. 4 shows a fringe scanning electron beam interference device.Only an exposure optical system, a sample to be measured, and anelectron beam biprism are shown for simplification. A vacuum containersystem including therein these components, a magnifying lens system, apower source system, and the like are not shown. Further, devicesnecessary for the measurement such as an image pickup element and acalculating device are the same as those in the laser interferencemeasuring device, and hence they are omitted.

[0031] A reference numeral 71 denotes an electron beam source, and areference numeral 72 is an electron beam emitted therefrom. The electronbeam 72 emitted from the electron beam source 71 is converted to anearly parallel beam through an exposure lens (exposure lens system) 73,and irradiated to a sample 74. The wavefront of the electron beam 72 isindicated by a solid line. The wavefront of the electron beam 72 ischanged in phase due to the distribution of thickness of the sample 74and the distribution of electromagnetic field inside and outside thesample upon passing through the sample 74, resulting in an unevenwavefront. The wavefront splitting element for electron interference isgenerally only an electron beam biprism. The electron beam biprism ismade up of oppositely disposed electrodes 75 and 76, and a thinelectrode 77 at the midpoint therebetween. The thin electrode 77 has afunction of drawing electron beams passing through its opposite sides,and superimposing the beams in the region therebeneath by theapplication with a voltage of about +100 V. Therefore, if the sample isplaced in either half of the electron beam path, the interference imageof the sample-transmitted wave and the reference wave is formed on anobserving plane 78. If the electron beam biprism is moved slightlyrightward as indicated by an arrow, the difference in progressing speedis caused between the wavefronts of the object wave and the referencewave as indicated by broken lines in the figure. As a result, thefringes in the interference image are moved. However, even if theelectron beam biprism is moved, the image of the sample is not movedbecause the tilt angle is constant. Therefore, the electron beaminterference measurement can also be carried out in the same manner aswith the laser interference. The phase distribution changed due to thesample can be measured by using the fringe scanning method, or theFourier transform method when the electron beam biprism is not moved.Incidentally, for the movement of the electron beam biprism, a piezoelement, a stepping motor, or the like is used as with the laserinterference measuring device, but it is not shown.

SUMMARY OF THE INVENTION

[0032] With any of the foregoing interference measuring methods, theerrors due to the interferometer itself are superimposed on themeasurement results. With these interferometries, the shift between thephase of the beam transmitted through, or reflected by a sample to bemeasured and the phase of a reference beam is measured. The factorsresponsible therefor in a laser interference system are the distortionof laser wavefront due to fluctuations of a laser light source,ununiformity of thickness distribution of a semitransparent mirror,unevenness of the reflecting mirror surface or the semitransparentmirror surface, and the like, fluctuations of air, inaccuracy ofthickness distribution of a biprism. The factors common to the laserinterference system and an electron beam interference system are thedistortion of a lens generated during manufacturing thereof, and Fresneldiffracted waves generated from the wavefront splitting boundary of thebiprism. The phase changes caused by the foregoing factors aresuperimposed on the phase changes due to the sample, to be originallymeasured. Out of these factors, the influence of the Fresnel diffractedwaves is the largest.

[0033] In the field of laser interference measurement, a reflection typeinterference system of roughly equivalent magnification is most oftenemployed. A transmission type interference system of roughly equivalentmagnification and a reflection type microscope are less often employed.Whereas, a transmission type microscope is employed very rarely. All ofthese are of an amplitude splitting type. There is no description on theinterference system of a wavefront splitting type in literatures. Withthe amplitude splitting type interference system, there is not includeda component for generating Fresnel diffracted waves as the wavefrontsplitting boundary, and it is possible to set each surface accuracy ofthe reflecting mirror and the semitransparent mirror at one-severaltenth the wavelength. Accordingly, the measurement error inherent in theinterference system is essentially small. Therefore, by using opticalcomponents having very high surface accuracy or thickness accuracy, themeasurement error inherent in the interference system is corrected basedon the phase distribution in the case where there is no sample for thetransmission-type interference system, or the very high precisionreference surface serving as a reference for the reflection typeinterferometer.

[0034] When the interference system of a transmission type microscope isconfigured, luminous fluxes split into two beams are required to includetheir respective magnifying lens systems, or to be received by the samemagnifying lens system. As a result, for the amplitude splitting type,the optical system is increased in size, and becomes complicated. Incontrast, for the wavefront splitting type, two luminous fluxes aresituated at a short distance from each other, and hence readily receivedby the same magnifying lens system. Therefore, the wavefront splittingmode is overwhelmingly advantageous in terms of the setting space andthe magnifying lens system. Particularly, for electron interference, theinterference element is only a wavefront splitting type electron beambiprism in terms of practicality.

[0035] However, with the wavefront splitting type interference element,the Fresnel diffracted waves from the wavefront splitting boundary verylargely affects the measurement. With the wavefront splitting typeinterference system, a beam is irradiated to the wavefront splittingelement. The wavefront splitting boundary is the portion where thedirection of refraction sharply changes for the laser interferencesystem. Whereas, for the electron beam interference system, it is madeup of a substance opaque (or having a transmittance largely differentfrom that of the vacuum portion) to an electron beam. Therefore, Fresneldiffracted waves are generated from this portion, and superimposed ontothe measurement region on the observing plane.

[0036]FIG. 5 schematically shows an example in which the phase changesdue to the Fresnel diffracted waves generated from the wavefrontsplitting boundary are generated by taking the biprism 5 of thewavefront splitting type fringe scanning laser interference measuringdevice of FIG. 1 as an example. For simplification, the wavefront of anobject wave 12 is indicated by a broken line, and the wavefront 16 ofFresnel diffracted wave on the object wave side is indicated by a solidline. The changes in phase due to an object are not shown. The laserlight to be irradiated onto a sample 10 is generally a plane wave, andhence expressed as a plane group as with the object wave 12. Only thesample-transmitted portion undergoes a change into uneven form, and theplane group which has undergone the change into uneven form passesthrough an objective lens 4, thereby to be converged to the objectivelens focal point. It further becomes a spherical wave divergingtherefrom, and passes through the biprism 5, which is a wavefrontsplitting element, thereby to be tilted. At this step, Fresneldiffraction occurs due to a crest 51 on the optical axis of the biprism5, so that wave in cylindrical plane from this point as a starting pointreaches the observing plane. The same occurs also for the referencewave. As a result, three waves of the object wave, reference wave, andFresnel diffracted wave interfere to one another on the observing plane.The Fresnel diffracted wave is divided into the Fresnel diffracted waveon the object wave side and the Fresnel diffracted wave on the referencewave side according to the shape and configuration of the wavefrontsplitting element 5, so that there occurs an interference of theresulting four waves. Therefore, the phase changes not due to the sampleare added to the measured results, and hence they cannot bediscriminated from the phase changes due to the sample.

[0037] Particularly, if the fringe scanning method which should becapable of higher-precision measurement is applied to the wavefrontsplitting type interference system, shifting in the relative positionalrelationship between the sample image and the interference fringes ismoving of the Fresnel diffracted wave because the interference fringesand the Fresnel diffracted wave are integral and inseparable.Accordingly, the measurement precision is unfavorably not improved asexpected in principle. As shown in FIG. 5, the Fresnel diffracted wavegenerated from the crest 51 at the center of the biprism 5 moves inconjunction with the movement of the biprism 5. Therefore, the changesin brightness at a given point P in the sample image are affected byboth the phase changes due to the sample and the phase changes due tothe Fresnel diffracted wave. This phenomenon invariably occursirrespective of the foregoing method for changing the relativepositional relationship between the sample image and the interferencefringes. Namely, the phase changes due to the optical system becomeinvolved in determining a sine curve, which causes the restriction onthe measurement precision.

[0038] This problem is also true for the interference measurement usingan electron beam. The thin electrode 77 of the electron beam biprismdescribed by reference to FIG. 4 is a substance opaque (or having atransmittance largely different from that of the vacuum portion) to anelectron beam. Therefore, Fresnel diffracted waves are generatedtherefrom. The influence of this phenomenon upon the measurement resultsis the same as described in the section on the laser interference.

[0039] Also with this method, by determining the difference in phasedistribution due to the presence or absence of the sample withprecision, it is possible to reduce the influence of the Fresneldiffracted wave to a certain degree. However, the Fresnel diffractedwave itself undergoes a phase change in the inside of the sample or inthe region where large phase changes occur. Therefore, it is notpossible to perform the correction with the difference in phasedistribution due to the presence or absence of the sample. Further, inactuality, a slight shift in the positional relationship between theoptical axis and a lens axis or the wavefront splitting element causesthe shift of the phase distribution due to the Fresnel diffracted waveon the observing plane. Therefore, it is not easy to obtain themeasurement data for the cases where there is the sample and there is nosample, under precisely identical conditions for a very short time.Accordingly, sufficient effects of correction often cannot be obtained.

[0040] Further, in electron interference, in many cases, the sample hasan electric field or a magnetic field, or a very small amount of chargesare accumulated in the sample. In such a case, the orbit of the electronbeam changes according to the presence or absence of the sample, so thatthe error inherent in the interference system also changes. Therefore,correction is rather counterproductive.

[0041] With the amplitude splitting type interference system, the slightshift in the positional relationship between the optical axis, and thelens axis or the interference system is the shift of the region to beused by the lens or the interferometer. In general, the differencetherebetween is sufficiently small. Further, for the laser interferencesystem, the amount to be measured is the distribution of refractiveindex for the laser light. Accordingly, the measurement results are notaffected at all even in the case where an electric field or a magneticfield is distributed around the sample. For such a reason, as distinctfrom the wavefront splitting type interference system, it is relativelyeasy to correct the measurement errors inherent with the interferencesystem with the measurement results for the case where there is nosample, and to achieve high measurement precision without a largedeficiency. However, with the wavefront splitting element, which isessentially very advantageous for a microscope, Fresnel diffracted wavesare inevitable in principle.

[0042] The foregoing problem become a large obstacle especially when awavefront splitting type interference system advantageous for atransmission type microscope is configured. However, this has beenscarcely recognized because there are very few examples of both theinterferometer using a wavefront splitting element and the transmissiontype interference measuring device. Whereas, the interferencemeasurement using an electron beam has only been performed verylimitedly. The fact that the Fresnel diffracted waves due to theelectron beam biprism adversely affects the measurement has not beenwidely recognized. Hitherto, there has been known only the method forperforming correction with the measurement results for the case wherethere is no sample.

[0043] In order to obtain precise measurement results in interferencemeasurement using a coherent beam (such as a laser light or an electronbeam), the measurement errors due to the interference system is requiredto be removed. Particularly, with the wavefront splitting typeinterference system, Fresnel diffracted waves are generated from thewavefront splitting boundary of the wavefront splitting element asdescribed above, which largely and adversely affects the measurementprecision.

[0044] The present invention has been completed for removing theinfluence of the Fresnel diffracted waves. Particularly, large effectsare produced for the wavefront splitting type interference microscopeand an electron interference microscope. The following second means iscapable of being applied also to a general amplitude splitting type orreflection type interference measuring device.

[0045] A first means for avoiding the problem is to prevent thegeneration of Fresnel fringes from the wavefront splitting boundary. Thewavefront splitting boundary is absolutely necessary. If there is theboundary, Fresnel diffraction invariably occurs. Therefore, to preventthe beam from being applied onto the boundary is the essential solvingmethod. Fresnel diffraction invariably occurs if there is some object,or if a wave undergoes a sharp change. The Fresnel diffracted waves areconverged into one point in the generation position or the opticallyequivalent position. The wavefront splitting element is required to beset at a different position from the sample plane and the observingplane, or the plane equivalent thereto in principle. Therefore, withthis, Fresnel diffracted waves are invariably superposed on theobserving plane.

[0046] Thus, if a shielding plate is placed on the plane equivalent tothe observing plane, to be formed between the laser light source and thebiprism, so that the wavefront splitting boundary of the wavefrontsplitting element lies within the shadow thereof, it is possible toavoid Fresnel diffracted waves by the shielding plate, and to implementthe situation where Fresnel diffraction will not occur at the wavefrontsplitting element.

[0047] In general, the measurement is carried out under the conditionwhere a focus is achieved on a sample. Therefore, in this case, theshielding plate is placed on the sample plane, or the plane equivalentto the sample plane, to be formed between the coherent beam source andthe wavefront splitting element. In this step, the shielding plate isnot required to be exactly on the observing plane, or the planeequivalent to the sample plane. Fresnel diffracted waves converge to onepoint at the source, and hence there occurs very little spreading ofFresnel diffracted waves in the very nearby region thereof. Therefore,the Fresnel diffracted waves due to the edges of the shielding plate isallowable so long as they do not affect the portion to be measured whichhas undergone phase changes due to the sample on the observing plane.

[0048] A second means for removing the phase changes due to theinterference system is the following method. Namely, two measurementresults for the case where there is a sample are obtained by shiftingthe positional relationship between the sample image and theinterference fringes. The difference between the two results isintegrated with respect to the direction of shift, thereby to obtain themeasurement result from which the errors inherent in the interferencesystem has been removed. Particularly, this method is combined with themethod referred to as a fringe scanning method wherein the phase changedistribution due to the sample is measured with high precision from aplurality of interference images having gradually and successivelyshifted relative positional relationships between the sample image andthe interference fringes with respect to each other. As a result, it ispossible to obtain high-precision correction effects with ease becausethe foregoing two types of measurement results can be obtained from aseries of interference image groups.

BRIEF DESCRIPTION OF THE DRAWINGS

[0049]FIG. 1 is a diagram showing an example of a configuration of awavefront splitting type fringe scanning laser interference measuringdevice;

[0050]FIG. 2.is a diagram schematically showing the manner in whichinterference fringes are formed and shifted;

[0051]FIG. 3 is a diagram schematically showing the fact that thebrightness of a given point P in interference images in which only theinterference fringes have been successively shifted in the laserinterference measuring system, changes in accordance with a sine curve;

[0052]FIG. 4 is a diagram showing an electron beam interference deviceusing a fringe scanning method;

[0053]FIG. 5 is a diagram schematically showing the phenomenon thatphase changes due to Fresnel diffracted waves are caused in a wavefrontsplitting type laser interference system;

[0054]FIG. 6 is a diagram showing an example of a configuration of afringe scanning laser interference measuring device based on themovement of a biprism, for illustrating an embodiment using a shieldingplate which is a first method of the present invention;

[0055]FIG. 7 is a diagram showing an example of a configuration of atwo-stage magnification type fringe scanning laser interferencemeasuring device based on the movement of a biprism, for illustratinganother embodiment using a mechanism for shifting the positionalrelationship between a sample and the interference fringes, andcalculation processing which is a second method of the presentinvention;

[0056]FIGS. 8A to 8D are diagrams respectively showing the examples ofthe prism shape applicable to the present invention, and the wavefrontsrespectively resulting therefrom;

[0057]FIG. 9 is a diagram showing an example of a configuration of anembodiment for implementing a fringe scanning method by micro-moving asample in place of the biprism;

[0058]FIG. 10 is a diagram showing an example of a configuration of anembodiment in which the fringe scanning method by electron beam tilt hasbeen applied to an electron beam interference measuring device;

[0059]FIGS. 11A to 11E are diagrams for schematically showing the stepsof one example of a method for forming an optical waveguide;

[0060]FIG. 12 is a view showing the observation result of the phasedistribution of the sliced cross section of an optical waveguide sample;and

[0061]FIG. 13 is a view showing the result obtained by observing theoptical waveguide from above, of which the observation result of thecross section is shown in FIG. 12.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0062] Embodiment 1

[0063] A first embodiment of the present invention will be described byreference to a fringe scanning laser interference measuring device basedon the movement of a biprism shown in FIG. 6. In this embodiment, abiprism 5 which is a wavefront splitting element was used as aninterference element, and a beam shielding plate 100 in such a form asto act as a shield against a beam to be irradiated to the wavefrontsplitting boundary of the biprism was disposed on the sample plane as ameans for removing the phase change distribution due to the interferenceelement. The phase distribution of a sample image or asample-transmitted beam is generally observed at the positive focalpoint. Herein, the shielding plate 100 was therefore placed on thesample plane equivalent to an observing plane, so that the positivefocal point image of a sample was formed directly on the image pickupsurface of an image pickup element 20. Herein, there was employed aone-stage magnifying system in which one lens was used between a sample10 and the wavefront splitting element 5. However, both a two- ormore-stage magnifying system and an optical system for furthermagnifying the interference image are also acceptable. When there isplaced a two-, or more-stage magnifying system before the wavefrontsplitting element, an intermediate magnified image is positioned on aplane equivalent to the observing plane. Accordingly, the shieldingplate 100 may also be placed thereon. With this arrangement, theshielding plate 100 may be enlarged, so that the requirement for theposition accuracy with respect to the shielding plate is also loosened.Thus, this process is desirable for a microscope. Whereas, the shieldingplate 100 may also be placed on a plane equivalent to an observing plane21 to be formed between a laser light source 1 and a collimator lens 3,although this arrangement is disadvantageous for being applied to amicroscope.

[0064] As indicated by the blank portion at the rear of the shieldingplate 100 in FIG. 6, in accordance with this embodiment, the wavefrontsplitting boundary 51 of the wavefront splitting element 5 causing thegeneration of Fresnel diffracted waves lies within the shadow of theshielding plate 100. Accordingly, it is possible to avoid Fresneldiffraction due to the wavefront splitting boundary 51. In this case,Fresnel diffracted waves are generated by the end face position of theshielding plate. However, as previously described, the waves will notaffect the portion changed in phase by the sample on the observingplane. The influences of Fresnel fringes generating from the wavefrontsplitting boundary becomes a more serious problem when a high-precisionmeasurement is carried out. Therefore, in this embodiment, the measuringsystem using a fringe scanning method was shown. However, needless tosay, even with a general interference measuring device which does notcontrol the relative positional difference between an object wave and areference wave, the effect of the beam shielding plate on themeasurement precision improvement is large.

[0065] Embodiment II

[0066]FIG. 7 shows a second embodiment of the present invention. This isso configured that the magnifying lens system of the fringe scanninginterference measuring device shown in FIG. 1 has been changed to atwo-stage system of an objective lens 4 and a magnifying lens 6 as faras the components shown in this figure concerned. Herein, a referencenumeral 25 denotes an intermediate magnified image, and 26 denotes theposition at which the intermediate magnified image is formed. A biprism5, which is a wavefront splitting element, was used as an interferenceelement. A biprism micro-movement mechanism 41 for shifting the relativepositional relationship between a sample image and the interferencefringes was disposed at an observing plane as a means for removing thephase change distribution due to the interference element. In addition,a calculating device 50 has functions of storing a first interferenceimage, and a second interference image shifted from the firstinterference image in the relative positional relationship between thesample image and the interference fringes, and determining the phasedistribution due to a sample to be measured by the interimage operationon a first phase distribution calculated from the first interferenceimage and a second phase distribution calculated from the secondinterference image. Further, with the device configuration in accordancewith the present invention, it is also possible to correct the phasechange amount due to an interferometer when the fringe scanning methodhas been used.

[0067] First, the most basic operation not using the fringe scanningmethod is as follow. The first interference image is formed with asample 10 being set, and one image thereof is inputted and stored in thecalculating device 50 via an image pickup element 20. As describedabove, this is mathematically Fourier transformed, and either of a+primary or a −primary spectrum is selected with an appropriate window,and Fourier inverse transformed to correct the tilt amount. Thus, thefirst phase distribution is determined. The determined first phasedistribution is the sum of both the following terms, and thus expressedas the following expression (5):

φ(x,y)+φ(x,y)  (5)

[0068] where φ(x,y) denotes the distribution of phase change due to thesample, and φ(x,y) denotes the phase distribution due to the largestFresnel diffracted wave, to only which a consideration is given forsimplification.

[0069] However, at this point, as with conventional devices and methods,it is not possible to discriminate between both phase distributions.

[0070] Then, the biprism 5 is moved in the direction orthogonal to boththe crest on the optical axis of the biprism and the optical axis, i.e.,in the upward direction or the downward direction on the figure by meansof a micro-movement control device 40 via a micro-movement controlmechanism 41 so that the interference fringes move by Δx on an observingplane 21. Thus, one image of the second interference image is capturedin the calculating device 50. In this example, the micro-movementcontrol device 40 is so configured as to be controlled by thecalculating device 50. However, the micro-movement control device 40 mayalso be controlled manually. As a result of movement of the biprism 5,the shift in the relative positional relationship between the sample andthe interference fringes is achieved. The phase distribution recorded inthe second interference image is calculated by the same operation asthat performed on the first interference image. The phase distributionherein reproduced is identical in phase change component due to thesample to the first phase change distribution. However, for the phasechange component due to Fresnel diffracted waves (and the biprism 5),the interference fringes move by Δx on the observing plane following themotion of the biprism 5. Therefore, the phase distribution determinedfrom calculation is expressed as the following expression (6):

φ(x,y)+φ(x+Δx,y)  (6)

[0071] Thus, the difference between the phase distribution calculatedfrom the second interference image and the phase distribution calculatedfrom the first interference image is determined, and the resulting valueis normalized by the amount of movement Δx. The amount thus obtained isexpressed as the following equation (7), which corresponds to the formof differentiation of the phase distribution due to Fresnel diffractedwaves with respect to the x direction: $\begin{matrix}{\frac{\left\{ {{\varphi \left( {x,y} \right)} + {\phi \left( {x,{\Delta \quad x},y} \right)}} \right\} - \left\{ {{\varphi \left( {x,y} \right)} + {\phi \left( {x,y} \right)}} \right\}}{\Delta \quad x} = \frac{{\phi \left( {{x + {\Delta \quad x}},y} \right)} - {\phi \left( {x,y} \right)}}{\Delta \quad x}} & (7)\end{matrix}$

[0072] Thus, if this is integrated with respect to the direction of Δx,it is possible to determine the phase distribution due to Fresneldiffraction as shown in the following equation (8): $\begin{matrix}{{\phi \left( {x,y} \right)} = {\int{\frac{{\phi \left( {{x + {\Delta \quad x}},y} \right)} - {\phi \left( {x,y} \right)}}{\Delta \quad x}{x}}}} & (8)\end{matrix}$

[0073] Thus, by determining the difference between the first phasedistribution expressed by the expression (5) and the phase distributionexpressed by the equation (8), it is possible to correct the errors dueto the interference system. As a result, it is possible to extract onlythe phase change distribution φ(x,y) due to the sample.

[0074] Strictly, the second phase distribution has a magnitude of thephase value shifted from that of the first phase distribution by thedifference in initial phase upon formation of the interference images.This is, however, achieved by shifting the contour of the phasedistribution in the direction of a phase axis as it is. Therefore, evenif this is translated in the direction of the phase axis, so that thelevels of the first and second phase distributions are in agreement witheach other, the results are not affected thereby at all. Further, thisamount is 2π×(amount shift of interference fringes Δx)/(distance betweeninterference fringes d). Therefore, it is also easy to correct thelevel.

[0075] In the laser interference system, prisms in various shapes may beadopted. FIGS. 8A to 8D show prisms in some shapes, to which the presentinvention can be applied, other than that in the foregoing embodiment,and the respective wavefronts caused thereby. In any case, the wavefrontsplitting boundary lies on the optical axis indicated by each dashedline. FIG. 8A shows a general triangular prism; FIG. 8B, an example inwhich a triangular prism set in such a direction that a beam diverges isused together with a condensing lens; and FIGS. 8C and 8D, a combinationof prisms each triangular in cross section with the wavefront splittingboundary as the interface. FIG. 8D shows only the element shape becausethe prism is used in the same manner as that of FIG. 8B.

[0076] The case where the fringe scanning method is applied in theembodiment shown in FIG. 7 is as follows.

[0077] While moving the biprism 5 so that the amount of movement of theinterference fringes with respect to the sample image is 1/M (M is apositive integer of larger than 3) of the distance between theinterference fringes on the observing plane 21, a first interferenceimage group made up of M images are inputted to the calculating device50. Then, while moving the biprism 5 in the same manner as describedabove so that the amount of movement of the interference fringes is 1/N(N is a positive integer of more than 3) of the distance between theinterference fringes from the state where the interference fringes havebeen shifted by Δx from the first interference image of the firstinterference image group, a second interference image group made up of Nimages are inputted to the calculating device 50. At this step, M and Nare not required to be identical with each other. The first phasedistribution can be calculated from the following equation (9) on eachpoint (x, y): $\begin{matrix}{{\frac{2\pi \quad x}{d} + {\varphi^{\prime}\left( {x,y} \right)}} = {\tan^{- 1}\left\lbrack \frac{\sum\limits_{m = 1}^{M}{{I\left( {x,{y;m}} \right)}{\sin \left( \frac{2\pi \quad m}{M} \right)}}}{\sum\limits_{m = 1}^{M}{{I\left( {x,{y;m}} \right)}{\cos \left( \frac{2\pi \quad m}{M} \right)}}} \right\rbrack}} & (9)\end{matrix}$

[0078] where the first term of the left side is the phase resulting fromthe interference of two tilted beams, and d denotes the distance betweenthe interference fringes; and the right side I(x,y;m) denotes thebrightness at point (x, y) in the m-th interference image in M images.

[0079] The phase distribution φ(x,y) obtained by correcting the phasedistribution of tilt is the same as the phase distribution of theexpression (5) determined in the foregoing manner, and expressed as thefollowing equation (10):

φ′(x,y)=φ(x,y)+φ(x,y)  (10)

[0080] Further, the second phase distribution determined similarly fromthe second interference image group can be calculated from the followingequation (11) given by replacing M and m in the equation (9) with N andn, respectively: $\begin{matrix}{{\frac{2\pi \quad \left( {x + {\Delta \quad x}} \right)}{d} + {\varphi^{\prime}\left( {{x + {\Delta \quad x}},y} \right)}} = {\tan^{- 1}\left\lbrack \frac{\sum\limits_{n = 1}^{N}{{I\left( {x,{y;n}} \right)}{\sin \left( \frac{2\pi \quad n}{N} \right)}}}{\sum\limits_{n = 1}^{N}{{I\left( {x,{y;n}} \right)}{\cos \left( \frac{2\pi \quad n}{N} \right)}}} \right\rbrack}} & (11)\end{matrix}$

[0081] As with the correction of the phase distribution of tilt withrespect to the first interference image group, the phase distributionφ′(x+Δx,y) obtained by correcting the phase distribution of tilt withrespect to the second interference image group is expressed as thefollowing equation (12):

φ′(x+Δx,y)=φ(x,y)+φ(x+Δx,y)  (12)

[0082] If the first phase distribution represented by the equation (10)is subtracted from the second phase distribution represented by theequation (12), and the resultant value is divided by Δx, as with theequation (7), it is possible to obtain the differential of the phasechange distribution due to the interference system as expressed by thefollowing equation (13): $\begin{matrix}{\frac{\left\{ {{\varphi \left( {x,y} \right)} + {\phi \left( {x,{\Delta \quad x},y} \right)}} \right\} - \left\{ {{\varphi \left( {x,y} \right)} + {\phi \left( {x,y} \right)}} \right\}}{\Delta \quad x} = \frac{{\phi \left( {{x + {\Delta \quad x}},y} \right)} - {\phi \left( {x,y} \right)}}{\Delta \quad x}} & (13)\end{matrix}$

[0083] Therefore, as with the foregoing equation (8), if this isintegrated with respect to the x direction, it is possible to determinethe phase change distribution φ(x,y) due to the interference system, inthis example, the phase changes due to the Fresnel diffracted wavesgenerated from the biprism. If this is subtracted from the value of theequation (10), it is possible to determine the phase change distributiondue to the sample. In this example, the laser interference system wasemployed. However, the device configuration is precisely the same evenfor the electron beam interference system shown in FIG. 4, so that it ispossible to implement the correction method only by the calculationprocessing.

[0084] Embodiment III

[0085] On the other hand, the second phase distribution of theexpression (6) is shifted by −Δx in the calculating device, andsubtracted from the first phase distribution of the expression (5). Theresultant value is then normalized by Δx. As a result, it is alsopossible to directly obtain the form given by differentiating the phasechange distribution due to the sample as expressed as the followingexpression (14): $\begin{matrix}\frac{{\varphi \left( {x,y} \right)} - {\varphi \left( {{x - {\Delta \quad x}},y} \right)}}{\Delta \quad x} & (14)\end{matrix}$

[0086] This is basically equivalent to that for the case where thesample 10 has been moved by −Δx in place of moving the biprism 5 ofEmbodiment 2 by +Δx for forming the second interference image except forthe opposite edges along the x direction of the image. Therefore, thesample 10 may also be moved. FIG. 9 shows an embodiment in which thefringe scanning interference method is implemented by micro-moving thesample 10. The configuration of FIG. 9 is different from theconfiguration of FIG. 6 only in that the micro-movement controlmechanism 41 vertically moves the sample 10 with respect to the opticalaxis 13 in place of the biprism 5, for easy understanding by comparisonwith that of FIG. 6. A signal is sent to the micro-movement controldevice 40 in response to an instruction via a calculating device 50 froman observer, so that the sample 10 can be vertically moved with respectto the optical axis 13. Also in this embodiment, it is possible tosimilarly perform the correction calculation of the device configurationand interference system errors even by a method based on the operationprocessing using Fourier transformation in place of the fringe scanningmethod.

[0087] First, an interference image is formed. While moving the sample10 so that the amount of movement of the sample is 1/M (M: a positiveinteger of larger than 3) of the distance between the interferencefringes on the observing plane 21, a first interference image group madeup of M images are inputted to the calculating device 50. Then, whilemoving the sample 10 so that the amount of movement of the sample 10 is1/N (N: a positive integer of more than 3) of the distance between theinterference fringes from the state where the sample position has beenshifted by Δx from that in the first interference image of the firstinterference fringe group, a second interference image group made up ofN images are inputted to the calculating device. As for the first phasedistribution, the amount of shift of the sample in each interferenceimage of the first interference image group is corrected in the oppositedirection in the calculating device, thereby to accomplish theconversion to the interference image group in which each position of thesample is aligned with that in the first interference image of thisgroup. Thus, the calculation is performed based on the equation (9).Also for the second phase distribution, similarly, each position of thesample in the second interference image group is corrected so as to beidentical with that in the first interference image of this group. Thus,the calculation is performed based on the equation (11). As a result,both are respectively as represented by the following expressions (15)and (16):

φ(x,y)+φ(x,y)  (15)

φ(x+Δx,y)+φ(x,y)  (16)

[0088] Therefore, if the first phase distribution is subtracted from thesecond phase distribution, and the resultant value is normalized withΔx, it is possible to directly determine the differential of the phasedistribution due to the sample 10 as expressed as the followingexpression (17). Accordingly, if integration is performed in the samemanner as with the equation (8), as expressed by the equation (17), itis possible to determine the phase distribution due to the sample.$\begin{matrix}\frac{{\varphi \left( {{x + {\Delta \quad x}},y} \right)} - {\varphi\left( \quad {x,y} \right)}}{\Delta \quad x} & (17)\end{matrix}$

[0089] Embodiment IV

[0090] If this method is further developed, a more systematicmeasurement is implemented. Examples of the procedure include somemethods as shown below.

[0091] A first method is a method in which an interference image groupof M+1 images recorded while successively shifting the relativepositional relationship between the sample image and the interferencefringes by 1/M (M is an integer≧3) of the distance therebetween iscaptured in the calculating device 50. The phase distribution determinedby calculation is determined as the values each indicating at whichposition each point is located with respect to the origin point of asine curve for the first interference image of each series. Therefore,the first phase distribution calculated using the first to M-th imagesof the interference images and the second phase distribution calculatedusing the second to M+1-th images are shifted in phase changedistribution due to the biprism from each other by 1/M of the distancebetween basic interference fringes along the direction orthogonal to thecrest on the optical axis of the biprism. They are shifted from eachother in absolute value of the phase value by 2π/M. Accordingly, thephase change distribution due to the sample can be determined directly,or after removing the errors inherent in the interference system fromthe first and second phase distributions by the same method as describedabove.

[0092] A second method is a method as follows: an interference imagegroup of M images recorded while successively shifting the relativepositional relationship between the sample image and the interferencefringes by 1/M (M is an even number of 6 or more) of the distancetherebetween on the observing plane 21 is captured in the calculatingdevice 50; and the first phase distribution calculated from theodd-numbered images of the interference image group and the second phasedistribution calculated from the even-numbered images of theinterference image group are used. The phase distributions calculatedfrom their respective images are shifted from each other in phase changedistribution due to the biprism by 1/M the distance. Accordingly, stillsimilarly, it is possible to extract only the phase change distributiondue to the sample.

[0093] A third method is implemented by extending the second method to acommon case. First, as an example, an interference image group of 12images recorded while successively shifting the interference fringes onthe observing plane by {fraction (1/12)} of the distance therebetweenare captured. Then, the captured images are classified into 3 sequencesin groups of 4-image series of {Image (1), Image (4), Image (7), Image(10)}, {Image (2), Image (5), Image (8), Image (11)}, and {Image (3),Image (6), Image (9), Image (12)}. Herein, Image (m) denotes the m-thinterference image. In the respective sequences, there are theircorresponding interference image groups each made up of 4 images havinginterference fringes successively shifted by {fraction (3/12)}(=¼) ofthe distance therebetween with respect to each other. Therefore, it ispossible to calculate the phase distributions by the phase shift methodin their respective series. The sequences are successively shifted fromeach other in initial phase by {fraction (1/12)} the distance.Therefore, if the difference between two phase distributions determinedfrom given two sequences out of the three sequences is determined, it ispossible to extract only the phase change distribution due to the samplein the same manner as described above.

[0094] For generalization, this can be expressed as follows. Namely,(K×M) interference images having interference fringes successivelyshifted by 1/(K×M) the distance with respect to each other are capturedin the calculating device, where M denotes a positive integer of 3 ormore, m is a variable (natural number) changing from 1 to M, K is apositive integer of 2 or more, and k is a variable (natural number)changing from 1 to K. Thus, there occur K sequences of interferenceimage groups each made up of M images expressed as the followingexpression:

ΣI{(m−1)K+k}  (18)

[0095] where Image {(m−1)K+k} denotes the ((m−1)K+k)-th interferenceimage.

[0096] It is possible to determine the phase distribution due to thesample from the first and second phase distributions respectivelycalculated from given two sequences out of the K sequences by any of theforegoing methods. For example, the Δx of the equation (4) is desirablysmaller from the mathematical viewpoint. However, it is desirably largerto a certain degree in actual data form from the viewpoint of effects ofa noise and the like. The optimum magnitude depends upon theexperimental conditions. However, when the phase distribution isdetermined from given two sequences out of the K sequences, it ispossible to set the Δx at 1/(KXM) of the distance between interferencefringes for the sequences where k=1 and k=2. Whereas, it is possible toset it at 2/(K×M) of the distance between interference fringes for thesequences where k=1 and k=3. This results in an increase in degree offreedom for selection of Δx. Further, even if a few interference imagesinappropriate to be used as data due to the factors such as vibrationand power source fluctuations are included in a sequence, substantialeffects are avoidable by using other two sequences except for thesequence for the calculation. In addition, such data acquisition can becarried out as the acquisition of a series of interference images.Therefore, this process will not cause more trouble.

[0097] Incidentally, needless to say, in the foregoing three methods,any of the mode of moving the biprism, the mode of moving the sample,and the mode of tilting the beam to be irradiated to the sample shown inEmbodiment 5 below can be used as the mode of shifting the relativepositional relationship between the sample image and the interferencefringes.

[0098] Embodiment V

[0099] A fifth embodiment is shown in FIG. 10. In the figure, the samecomponents as those of the electron interference measuring devicedescribed by reference to FIG. 4 are provided with the same referencenumerals. This device is implemented by applying the fringe scanningmethod based on an electron beam tilt to the electron interferencemeasuring device, and shown in cross section along the electron beamaxis. For simplification, only the outline from an electron beam sourceto an intermediate magnified surface is shown, and an electron opticalsystem unnecessary for describing the principle, the details of themicro-movement mechanism of an electron beam biprism, a vacuumcontainer, a magnifying lens system behind the intermediate magnifiedsurface, power sources of an acceleration voltage, a lens, and adeflection system, and the like are omitted. Although there is anobjective lens between the sample and the intermediate magnifiedsurface, it is omitted in the figure because the optical system becomescomplicated. Further, the instruments necessary for observation andmeasurement are the same as those of Embodiment 1. Therefore, these arealso omitted. In Embodiment 5, as a means for removing the phase changedistribution due to the interference element, there are included amechanism for shifting the relative positional relationship between thesample image and the interference fringes on the observing plane bychanging the tilt of the electron beam to be irradiated to the sample74, and a calculating device (not shown) having functions of storing afirst interference image, and a second interference image sifted in therelative positional relationship between the sample image and theinterference fringes from the first interference image, and determiningthe phase distribution due to the sample to be measured by theinterimage operation on a first phase distribution calculated from thefirst interference image and a second phase distribution calculated fromthe second interference image.

[0100] The electron beam 72 emitted from the electron beam source 71 isconverted to a generally parallel beam by using the exposure lens 73,and the resulting beam is irradiated to the sample 74 placed in eitherhalf of the electron beam path. The electron beam transmitted throughthe sample 74 forms an image on the intermediate magnified surface 78 byan objective lens (not shown). The electron beam biprism made up of athin central electrode 77 and a pair of flat ground electrodes 75 and 76is placed between the objective lens and the intermediate magnifiedsurface 78. The electron beams passed through the opposite sides of thecentral electrode 77 applied with a voltage of about +100 V are drawn bythe electric field, and superimposed one on another in the regiontherebeneath. Therefore, a sample-side electron beam 92 (plane groupslanting upwardly to the left) passed through the sample and asample-less side reference electron beam 93 (plane group slantingupwardly to the right) interfere with each other to form an interferenceimage made up of linear interference fringes only of which the sampleimage portion has undergone displacement on the intermediate magnifiedsurface 78. At this step, Fresnel diffracted waves 17 are generated fromthe opposite sides of the thin electrode 77 of the electron beambiprism, and superimposed on the interference image.

[0101] A pair of upper and lower electron deflection systems are placedbetween the exposure lens 73 and the sample 74. The deflection systemsare made up of an upper deflection system for effecting a magnetic fieldgoing from the back to the front of the paper plane as indicated by areference numeral 95, and deflecting the electron beam rightward by agiven angle on the paper plane as indicated by an arrow 97; and a lowerdeflection system for effecting a magnetic field going from the front tothe back of the paper plane as indicated by a reference numeral 96,deflecting the electron beam leftward as indicated by an arrow 98 on thepaper plane to undo the amount of deflection due to the upper deflectionsystem, and making unchangeable the position of the sample plane throughwhich the electron beam passes. Namely, a pair of the upper and lowerelectron beam deflection systems are configured so that the electronbeam can be changed in angle of incidence to the sample 74 around thesample plane transmitting position as the rotation center when theelectron beam passing through the portion of the sample 74 is expressedas a straight line. Herein, for easy observation in a schematic mannerof the respective states of the deflected electron beam, an envelope inbroken line is given, and the shift of the wavefront of the electronbeam is shown by a broken line.

[0102] The central electrode 77 of the electron beam biprism andinterference fringes formed on the intermediate magnified surface 78 arealong the direction of the normal to the paper plane of the figure. Ifthe rotation of the electron beam around the electron beam axis due tothe objective lens is neglected for simplification, the electron beam isrequired to be deflected laterally in the figure for moving theinterference fringes in the direction orthogonal to the direction of thefringes. For this, the deflection magnetic field must be along thedirection of the normal to the paper plane.

[0103] In general, a magnetic field type of deflection system is used.However, if a coil or a magnetic path is shown, the figureinconveniently becomes complicated. Therefore, for the electron beamdeflection system, only the generating magnetic field is shown as itsdirection. First, with the upper electron beam deflection system, amagnetic field going upwardly along the direction of the normal to thepaper plane 95 is generated to deflect the electron beam rightward asindicated by a broken line. The lower electron beam deflection systemgenerates a magnetic field going downwardly along the direction of thenormal to the paper plane 96. In addition, the intensity of the magneticfield is adjusted so that the position of the sample through which theelectron beam passes is unchanged before and after the deflection. Asindicated by the broken line, the orbit of the electron beam is shiftedas compared with that of the electron beam before deflection, and passesthrough different positions of the objective lens 81 and the electronbeam biprism. However, as indicated from the fact that the scatteredwaves diverging from one point of the sample converge to one point onthe image surface, the position of the sample through which the electronbeam passes is unchangeable before and after deflection. Therefore, theimage of the sample will not move. On the other hand, the irradiationdirection to the electron beam biprism is tilted in the same manner asindicated by the arrow 98. Therefore, the center of the interferencefringe group is shifted from on the electron beam onto the extensionline connecting between the electron beam source and the centralelectrode. Accordingly, the interference fringes shift to the left withrespect to the sample image in this case. The Fresnel diffracted wavesgenerating from impingement of the electron beam on the centralelectrode are also shifted similarly in accordance with the shift of theirradiation direction.

[0104] While changing the amount of deflection of the electron beam sothat the interference fringes are successively shifted by 1/M of thedistance therebetween on the intermediate magnified surface 78 or theobserving plane not shown, a total of M interference images are capturedin a calculating device not shown. As a result, it becomes possible toperform the phase distribution calculation by the fringe scanning methodin the same procedure as described above. Thus, herein, it is possibleto carry out the present invention by using the already described methodwherein (M+1) interference images successively shifted in the positionsof the interference fringes by 1/M the distance with respect to eachother are captured, or method wherein (K×M) (K is 2, M is a positiveinteger of 3 or more) interference images are captured, and these aredivided into M×K sequences of interference image groups.

[0105] In this embodiment, the relative positional relationship betweenthe sample and the interference fringes is shifted by changing the anglefor sample irradiation. However, as described previously by reference toFIG. 4, needless to say, even if the foregoing operation is carried outby changing the positions of the electrodes 75, 76, and 77, or only theposition of the central electrode 77 of the electron beam biprism, thesame effects can be obtained to carry out this embodiment.

[0106] In this embodiment, the electron beam passes different positionsof the objective lens, the electron beam biprism 75 to 77, and otherelectron-optical elements present in the regions other than on the planeequivalent to the sample plane not shown. Accordingly, all the phasechanges resulting therefrom are shifted in accordance with the shift ofthe interference fringes. Therefore, it is possible to correct all thephase changes due to not only the electron beam biprism but also theelectron-optical systems present behind the sample plane and in theregions other than the plane equivalent with the sample plane.

[0107] The electron beam deflection system for changing the angle of theincident electron beam around the sample incidence point as the centeris operated in the following two manners. A first method is as follows.The ratio of the respective numbers of turns of the coils is determinedso that the respective amounts of deflection due to the upper and lowercoils determined according to the positional relationship between theupper and lower coils and the sample are equal to each other. Connectionin series is established so that the respective magnetic fieldsgenerated by the upper and lower coils are mutually opposite indirection. Thus, a current is supplied from one direct current source. Asecond method is as follows. The upper and lower coils are respectivelyconnected to different current sources, and thereby individuallyoperated with an appropriate current ratio. Further, both of the methodsmay also be employed in combination. Herein, the electron beamdeflection systems have been described as if they are of one system.However, even the deflection system of x-y two systems is acceptablewithout any inconvenience so long as it is capable of moving theinterference fringes in the direction orthogonal to the directionthereof.

[0108] Incidentally, the exposure lens system 73 is, in most cases, madeup of two-stage or three-stage electron lenses. However, in thisdescription, only one stage is shown for illustration. Further, needlessto say, there is no change in principle even if there is another one-,or more-stage magnifying lens between the objective lens and theelectron beam biprism.

[0109] The case where the method for tilting the beam is implemented bya laser interferometer is different from the foregoing case in principleand mechanism for tilting the beam. However, apparently, it is identicalthereto in terms of the following aspects: occurrence of shift in theposition through which the beam passes and the interference fringes; theresultant applicability of the present invention; the merit that it isalso possible to correct the phase changes due to optical componentssituated behind the sample plane and in regions other than the planeequivalent to the sample plane together; etc.

[0110] Up to this point, the following method has been described.Namely, the phase distribution due to the sample and the phasedistribution due to the interferometer are separated from each otherfrom the difference between the first and second phase distributionsrespectively calculated from the first and second interference image(groups) having mutually shifted relative positional relationships eachbetween the sample image and the interference fringes. The fundamentalrequirement for this method is that only either of the phasedistribution due to the sample and the phase distribution due to theinterferometer is shifted in accordance with the shift in the relativephase relationship. This corresponds to the lateral shift in thepositional relationship between the sample and the optical systemcomponents not directly involved in the formation of the sample image.Therefore, also in general interference systems such as the Michelsoninterferometer shown in FIG. 1 on page 56 of the reference literature 1and the Mach-Zehnder interferometer shown in FIG. 1 of the referenceliterature 3, if the reflecting mirror, the semitransparent mirror, orthe like is laterally shifted, only the phase change due to thecomponent is laterally shifted with respect to the sample image.Further, as shown for the electron beam interference system, if the tiltof the beam to be irradiated to the sample is changed, only the phasechange due to the interference system is shifted because the beam passesthrough the different positions of the optical components not situatedon the sample plane or its equivalent plane. Namely, even in anyinterference measuring device, if a mechanism for laterally shifting thepositional relationship between the sample and the optical systemcomponents not directly involved in the formation of the sample image isincluded, and a calculation processing is performed on the first andsecond phase distributions calculated from the first and secondinterference image (groups) having mutually shifted in the positionalrelationship in accordance with the foregoing method, it is possible toseparate and extract the phase change due to the sample and the phasechange due to the interference system. (Application to evaluation ofwaveguide)

[0111] Below, in order to evaluate an optical waveguide by means of theinterference measuring device in accordance with the present invention,a description will be given to an application example in which therefractive index distribution of the cross section of the opticalwaveguide is measured.

[0112]FIGS. 11A to 11E are views schematically showing one example of amethod for forming an optical waveguide. First, as shown in FIG. 11A, aquartz substrate 201 is prepared. As shown in FIG. 11B, on the substrate201, a (SiO₂+TiO₂) layer 202 with a prescribed thickness, which will bethe optical waveguide, is formed. The amount of TiO₂ is selected to beabout 1 Wt % so that the difference in refractive index between thesubstrate 201 and the optical waveguide layer 202 is 0.3%. On the(SiO₂+TiO₂) layer 202, a mask is formed with a resist layer, and onlythe linear region of the resist layer corresponding to the opticalwaveguide is left by photolithgraphy, and reactive ion etching (RIE) isperformed thereon to form an optical waveguide 203 as shown in FIG. 1C.Then, as shown in FIG. 1D, a layer 204 of SiO₂ particles containingphosphorus (P) and boron (B) as dopants is deposited thereon by FHD(flame hydrolysis deposition). Finally, the whole is subjected to a heattreatment at about 1200° C., thereby to make transparent the whole 205of the substrate 201 and the deposition layer 204.

[0113] P and B doping reduces the softening temperature. P has afunction of increasing the refractive index, and B has a function ofdecreasing the refractive index. Therefore, the amounts of P and Bcontained in the deposition layer 204 are controlled so that softeningof the substrate 201 and the optical waveguide 204 during the heattreatment for higher transparency is minimized, and so that therefractive index of the deposition layer 204 becomes equal to that ofthe substrate 201.

[0114] As the characteristics of the optical waveguide, desirably, therefractive index sharply changes at the boundary of the waveguideportion, so that optical signals are localized into the waveguide.However, there are pointed out the possibility that the particlescontaining P in larger amounts first soften, when the deposition layer204 softens during the manufacturing process, to form a P-rich layer atthe boundary with the substrate 201 and the possibility that therefractive index distribution is broadened by diffusion of addedcomponents. However, hitherto, the measurement of such a refractiveindex distribution has been carried out in the following manner. Forexample, how much the transmitted optical signal is attenuated at theoutput side is determined. Alternatively, an observation is performedunder an interference microscope, so that a judgment is made based onthe manner in which the interference fringes are curved. Therefore,these methods cannot be said to be adequate evaluation methods.

[0115] However, if the present invention is applied thereto, it ispossible to directly observe and measure the refractive indexdistribution. First, for description of the observation principle, aconsideration will be given to the phase change resulting from thedifference in refractive index. The number of waves N present in awaveguide is represented by the following equation (19): $\begin{matrix}{N = \frac{t}{\lambda_{2}}} & (19)\end{matrix}$

[0116] where n₂ denotes the refractive index of the waveguide, t denotesthe thickness along the optical path of the waveguide, and λ₂ denotesthe wavelength of a laser light within the waveguide. If it is assumedthat the refractive index of the clad portion is n₁, and the wavelengththereof is λ₁, the phase shift per period of the wave is represented ona wavelength basis by the following expression (20): $\begin{matrix}\frac{\lambda_{1} - \lambda_{2}}{\lambda_{1}} & (20)\end{matrix}$

[0117] The refractive index n of a substance is expressed as the ratioof wavelength λ in the substance to wavelength λ₀ in vacuum, i.e., thefollowing equation (21): $\begin{matrix}{n = \frac{\lambda_{0}}{\lambda}} & (21)\end{matrix}$

[0118] Therefore, the phase shift Δφ [rad] when the light has passedthrough the waveguide is expressed as the following equation (22):$\begin{matrix}\begin{matrix}{{\Delta\varphi} = \frac{2\pi \quad {N\left( {\lambda_{1} - \lambda_{2}} \right)}}{\lambda_{1}}} \\{= {2\pi \frac{t}{\lambda_{1}}\frac{\lambda_{1} - \lambda_{2}}{\lambda_{2}}}} \\{= {2\pi \quad t\frac{n_{2} - n_{1}}{n_{1}}\frac{n_{1}}{\lambda_{0}}}}\end{matrix} & (22)\end{matrix}$

[0119]FIG. 12 is the observation result of the sliced cross section ofan optical waveguide sample. The contour lines are drawn for every{fraction (1/10)} the wavelength phase change. A 5-μm scale is shown inthe right-hand corner under the figure. The bottom side of the generallyrectangular shape is the interface with the quartz substrate 201. Thedifference in refractive index between the waveguide central portion 203and the clad layer 205 is 0.3% for this sample. Therefore, it ispossible to read the difference in refractive index of about 5×10⁻⁵ fromthe phase distribution. This enables the close measurements of theuniformity of the refractive index within the waveguide or within thetransparent layer, and the like.

[0120]FIG. 13 is a view showing the result obtained by observing theoptical waveguide from above, of which the observation result of thecross section is shown in FIG. 12. The dark band region is the waveguide203. The graph shown in the lower column in the figure shows the phaseprofile of the region at the position indicated by arrows shown in theleft and right margins of FIG. 13. It is possible to read the phasechange amount of each region from the profile. Therefore, it is possibleto measure the distribution of the refractive index from the equation(22) if the refractive index of the clad portion is known.

[0121] In accordance with the first method of the present invention, itbecomes possible to remove the phase change due to the Fresneldiffracted waves generated from the wavefront splitting boundary of thebiprism in the interference measuring device belonging to the wavefrontsplitting type, or the Fresnel diffracted waves in the interferencemeasuring device using an electron beam in the following manner. Namely,a beam shielding plate in such a form as to shield the wavefrontsplitting boundary is set on the plane equivalent to the observingplane, to be formed between the coherent beam source and the biprism.Further, in accordance with the second or third method of the presentinvention, the removal can be performed mathematically from the twophase distribution data respectively obtained from the two sequences ofinterference image (groups) mutually shifted in relative positionalrelationship between the sample and the interference fringes.

What we claim is:
 1. An interference measuring device, comprising: acoherent beam generating source; a sample to be measured; a lens systemfor forming an image of the sample to be measured on an observing plane;an interference element for splitting a coherent beam into two systems,and forming an interference image on the observing plane or a planeequivalent thereto; an image pickup element for picking up theinterference image on the observing plane; a calculating device havingfunctions of capturing and storing the interference image converted toelectric signals by the image pickup element, and determining the phasedistribution changed by the sample to be measured from the interferenceimage by calculation; and a means for removing the phase changedistribution due to the interference element.
 2. The interferencemeasuring device according to claim 1, wherein the interference elementis a wavefront splitting element, and the means for removing the phasechange distribution due to the interference element is a beam shieldingplate in such a form as to act as a shield against a beam to beirradiated to the wavefront splitting boundary of the interferenceelement on a plane equivalent to the observing plane between thecoherent beam generating source and the interference element, or in thevicinity thereof.
 3. The interference measuring device according toclaim 1, wherein the means for removing the phase change distributiondue to the interference element is a mechanism for shifting the relativepositional relationship between a sample image and interference fringeson the observing plane, and the calculating device has functions ofstoring a first interference image, and a second interference imageshifted in relative positional relationship between the sample image andthe interference fringes from the first interference image, anddetermining the phase distribution due to the sample to be measured bythe interimage operation on a first phase distribution calculated fromthe first interference image and a second phase distribution calculatedfrom the second interference image.
 4. The interference measuring deviceaccording to claim 1, wherein the means for removing the phase changedistribution due to the interference element is a mechanism for shiftingthe relative positional relationship between a sample image andinterference fringes on the observing plane, and the calculating devicehas functions of storing a first interference image group, and a secondinterference image group starting from an interference image shifted inrelative positional relationship between the sample image andinterference fringes from the first interference image of the firstinterference image group, and determining the phase distribution due tothe sample to be measured by the interimage operation on a first phasedistribution calculated from the first interference image group and asecond phase distribution calculated from the second interference imagegroup.
 5. The interference measuring device according to claim 3 or 4,wherein the means for removing the phase change distribution due to theinterference element is a mechanism for shifting the relative positionalrelationship between a sample image and interference fringes on theobserving plane, and the calculating device has a function ofintegrating a difference image obtained by shifting at least one of thefirst phase distribution and the second phase distribution in phase orposition, and then calculating the difference therebetween with respectto the direction of shift of the positional relationship between thesample image and an interference image, and thereby determining thephase distribution due to the interference element or the phasedistribution due to the sample to be measured, or both of them.
 6. Theinterference measuring device according to claim 1 or 2, wherein theinterference element is a wavefront splitting element, the means forremoving the phase change distribution due to the interference elementis a beam shielding plate in such a form as to act as a shield against abeam to be irradiated to the wavefront splitting boundary of theinterference element on a plane equivalent to the observing planebetween the coherent beam generating source and the interferenceelement, or in the vicinity thereof, and a means for shifting therelative positional relationship between the sample image andinterference fringes on the observing plane is included.
 7. Theinterference measuring device according to any of claims 3, 4, 5, and 6,wherein the mechanism for causing a shift in the relative positionalrelationship between the sample image and the interference image movesthe interference element.
 9. The interference measuring device accordingto any of claims 3, 4, 5, and 6, wherein the mechanism for causing ashift in the relative positional relationship between the sample imageand the interference image changes the tilt of a coherent beam to beirradiated to the sample.
 10. The interference measuring deviceaccording to any of claims 3, 5, and 6, wherein the mechanism forcausing a shift in the relative positional relationship between thesample image and the interference image moves the sample within a planeorthogonal to the optical axis, and in a memory of the calculatingdevice, the data of position of any of the first phase distribution andthe second phase distribution is shifted in the direction of shift inthe relative positional relationship between the first interferenceimage and the second interference image by the shift amount.
 11. Theinterference measuring device according to any of claims 4, 5, and 6,wherein the mechanism for causing a shift in the relative positionalrelationship between the sample image and the interference image movesthe sample within a plane orthogonal to the optical axis, and in amemory of the calculating device, the data of position of any of a firstphase distribution calculated after aligning the sample position in eachinterference image of the first interference image group with that inthe first interference image of the group and a second phasedistribution calculated after aligning the sample position in eachinterference image of the second interference image group with that inthe first interference image of the group is shifted in the direction ofshift in the relative positional relationship between the firstinterference image of the first interference image group and the firstinterference image of the second interference image group by the shiftamount.
 12. The interference measuring device according to any of claims4, 5, 7, 8, 9, and 11, wherein the interference fringes on the observingplane are successively shifted by 1/M, (M≧3) of the distancetherebetween to record an (M+1)-interference-image group, and a firstinterference image group is set to include the first to M-th images ofthe (M+1)-interference-image group, and a second interference imagegroup is set to include the second to (M+1)-th images of the(M+1)-interference-image group, where M is a positive integer of 3 ormore.
 13. The interference measuring device according to any of claims4, 5, 7, 8, 9, and 11, wherein (K×M) interference images havingpositional relationships each between the interference fringes and thesample successively shifted by 1/(K×M) with respect to each other, whereK is a positive integer of 2 or more, k is a variable changing from 1 toK, M is a positive integer of 3 or more, and m is a variable changingfrom 1 to M, are sequentially captured in the calculating device suchthat respective numbers are understandable; the interference imageshaving their respective numbers each represented by the relationalexpression of {(m−1)K+k}, for k being from 1 to K, where m is from 1 toM, are grouped, and thereby classified into K sequences of interferenceimage groups; and the given two sequences of the K sequences ofinterference image groups are set to be the first interference imagegroup and the second interference image group.
 14. The interferencemeasuring device according to any of claims 1 to 13, wherein thecoherent beam is a laser light; an interferometer is a pole-like prismhaving a triangular cross sectional shape, or a cross sectional shapemade up of combined triangles with the wavefront splitting boundary asthe boundary therebetween; and the lens system is an optical lenssystem.
 15. The interference measuring device according to any of claims1 to 13, wherein the coherent beam is an electron beam, theinterferometer is an electron beam biprism, and the lens system is anelectron lens system.